Question

[tex] \frac{24}{18-x}-\dfrac{24}{18+x}= 1[\tex]

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Answer 1

$\huge \cal \underline \color{red}★A᭄ɴsᴡΣʀ࿐$

Answer 2

$\frac{24}{18 - x} - \frac{24}{18 + x} = 1$

$\frac{24(18 + x) - 24(18 - x)}{(18 - x)(18 + x)} = 1$

$\frac{432 + 24x - 432 + 24x}{ {(18)}^{2} - {(x)}^{2} } = 1$

$\frac{48x}{324 - {x}^{2} } = 1$

$48x = 324 - {x}^{2}$

$48x + {x}^{2} = 324$

Using quadratic formula we get,

$x = \frac{ - 48± \sqrt{ {48}^{2} + 1296 } }{2} = \frac{ - 48± \sqrt{3600} }{2}$

$= \frac{ - 48±60}{2} = 6 \: or \: - 54$